# Ez.eqn7.supp: Expectation of z given y, beta2, phi In RobinHankin/calibrator: Bayesian Calibration of Complex Computer Codes

## Description

Expectation as per equation 7 on the supplement

## Usage

 `1` ```Ez.eqn7.supp(z, D1, H1, D2, H2, extractor, beta2, y, E.theta, phi) ```

## Arguments

 `z` Vector of observations `D1` Matrix whose rows are code run points `H1` Regressor basis functions `D2` Matrix whose rows are observation points `H2` Regressor basis functions `extractor` Function to split D1 `beta2` coefficients `y` Code outputs at points corresponding to rows of `D1` `E.theta` Expectation function to use `phi` hyperparameters

## Author(s)

Robin K. S. Hankin

## References

• M. C. Kennedy and A. O'Hagan 2001. Bayesian calibration of computer models. Journal of the Royal Statistical Society B, 63(3) pp425-464

• M. C. Kennedy and A. O'Hagan 2001. Supplementary details on Bayesian calibration of computer models, Internal report, University of Sheffield. Available at http://www.tonyohagan.co.uk/academic/ps/calsup.ps

• R. K. S. Hankin 2005. Introducing BACCO, an R bundle for Bayesian analysis of computer code output, Journal of Statistical Software, 14(16)

`V.fun`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```data(toys) etahat.d2 <- etahat(D1=D1.toy, D2=D2.toy, H1=H1.toy, y=y.toy, E.theta=E.theta.toy, extractor=extractor.toy, phi=phi.toy) beta2 <- beta2hat.fun(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, V=V.toy, z=z.toy, etahat.d2=etahat.d2, extractor=extractor.toy, E.theta=E.theta.toy, Edash.theta=Edash.theta.toy, phi=phi.toy) Ez.eqn7.supp(z=z.toy, D1=D1.toy, H1=H1.toy, D2=D2.toy, H2=H2.toy, extractor=extractor.toy, beta2=beta2, y=y.toy, E.theta=E.theta.toy, phi=phi.toy) ```